Document Type : Research Paper
Authors
1 Department of Mathematics, Babol Noshirvani University of Technology, Shariati Ave., Babol, Iran
2 Department of Mathematics, Yazd University, Iran
Abstract
In this paper, we discuss the structure of intuitionistic fuzzy projec- tive modules and investigate some properties of them. Also we study about intuitionistic fuzzy homomorphisms between intuitionistic fuzzy modules.
We study about exact sequences, products and co-products, func- tors and relating topics in IFR − Mod and investigate the relationship between them, where IFR − Mod is category whose objects are intu- itionidtic fuzzy modules and morphisms are intuitionistic fuzzy homo-
morphisms.
For a commutative ring R and two intuitionistic fuzzy R- modules
A = (μA, νA) ≤IF M, B = (μB, νB) ≤IF N we show that
HomIF −R (A, B) = (α, β) is an intuitionistic fuzzy R-module.
Also for a commutative ring R, if
0⟶𝐴𝑓~→ B 𝑔~→ C is an exact sequence in IFR-Mod, where f˜ is IF split homomorphism, then
we show that HomIF −R(D,-) preserves the sequence, for every D ∈ IFR − Mod.
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